Complementarity in classical dynamical systems

Details Complementarity in classical dynamical systems Complementarity in classical dynamical systems

2004-07-20

arxiv.org/abs/nlin/0407046v5

Foundations of Physics 36, 291-306 (2006)

Nonlinear Sciences

Chaotic Dynamics

18 pages, no figures

Scientific paper

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.

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